Quantum spin amplification
A method for quantum spin amplification includes spin-polarizing an ensemble of quantum spins in an initial spin state to generate a transversely-polarized sensing spin state. The quantum spins identically have an upper energy state and a lower energy state. The sensing spin state accumulates a phase shift that transforms the sensing spin state into a phase-accumulated spin state having first and second transverse polarization components. The phase-accumulated spin state is transformed into an intermediate spin state by rotating the first transverse polarization component into a longitudinal polarization component of the intermediate spin state. The ensemble is then coupled to an auxiliary mode, during which the intermediate spin state evolves such that the second transverse polarization component is amplified into an amplified transverse polarization. This amplified transverse polarization is then measured.
1. A method for quantum spin amplification, comprising:
spin-polarizing an ensemble of quantum spins in an initial spin state to generate a sensing spin state that is transversely polarized with respect to a quantization axis, the quantum spins identically having an upper energy state and a lower energy state;
accumulating, by the sensing spin state, a phase shift that transforms the sensing spin state into a phase-accumulated spin state having first and second transverse polarization components that are orthogonal to each other, the phase shift being based on an energy spacing between the upper and lower energy states;
transforming the phase-accumulated spin state into an intermediate spin state by rotating the first transverse polarization component into a longitudinal polarization component of the intermediate spin state;
coupling the ensemble of quantum spins to an auxiliary mode, wherein the intermediate spin state, in response to said coupling, evolves such that the second transverse polarization component is amplified into an amplified transverse polarization; and
measuring the amplified transverse polarization.
2. The method of claim 1 , wherein:
said coupling induces collective dissipation of the ensemble of quantum spins; and
the intermediate spin state, in response to the collective dissipation, undergoes superradiant decay that amplifies the second transverse polarization component into the amplified transverse polarization.
3. The method of claim 1 , wherein:
said coupling induces non-dissipative collective dynamics of the ensemble of quantum spins and the auxiliary mode; and
the intermediate spin state coherently evolves in response to the non-dissipative collective dynamics.
4. The method of claim 1 , wherein said measuring comprises measuring the amplified transverse polarization along a measurement axis orthogonal to the quantization axis.
5. The method of claim 1 , wherein said measuring comprises:
rotating the amplified transverse polarization into an amplified longitudinal polarization; and
measuring the amplified longitudinal polarization along the quantization axis.
6. The method of claim 1 , wherein:
the upper and lower energy states are degenerate in the absence of an external electromagnetic field; and
the external electromagnetic field lifts the degeneracy of the upper and lower energy states.
7. The method of claim 1 , wherein the upper and lower energy states are non-degenerate energy eigenstates of the quantum spins.
8. The method of claim 1 , wherein said transforming the phase-accumulated spin state includes applying a pulse to the ensemble of quantum spins to rotate the phase-accumulated spin state around a rotation axis that is orthogonal to the quantization axis.
9. The method of claim 1 , wherein said spin-polarizing includes applying a pulse to the ensemble of quantum spins to rotate the initial spin state around a rotation axis that is orthogonal to the quantization axis.
10. The method of claim 1 , wherein the quantum spins identically have a spin quantum number equal to ½.
11. The method of claim 1 , wherein the quantum spins identically have a spin quantum number that is greater than ½.
12. The method of claim 1 , wherein the auxiliary mode is, or approximates, a bosonic mode.
13. The method of claim 12 , wherein the bosonic mode is a lossy bosonic mode.
14. The method of claim 13 , wherein said coupling includes strongly coupling the ensemble of quantum spins to the lossy bosonic mode.
15. The method of claim 1 , further comprising applying, during said coupling, a dynamical decoupling sequence to the ensemble of quantum spins.
16. The method of claim 1 , wherein said coupling includes coupling the ensemble of quantum spins to a resonant mode of a photonic cavity.
17. The method of claim 16 , wherein said coupling includes:
turning on the collective dissipation by controlling the photonic cavity such that a transition between the upper and lower energy states is resonant with the resonant mode; and
turning off the collective dissipation by controlling the photonic cavity such that the transition is not resonant with the resonant mode.
18. The method of claim 1 , wherein said coupling the ensemble of quantum spins to an auxiliary mode includes coupling the ensemble of quantum spins to a mechanical mode.
19. The method of claim 1 , wherein the quantum spins are selected from the group consisting of atoms, ions, nuclear spins, solid-state spins, nitrogen vacancy defect centers, silicon vacancy defect centers, and superconducting qubits.
20. A system for quantum spin amplification, the system being operable to perform the method of claim 1 .